Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3nw)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=11/8, b>=a

For fixed z and a=11/8, b=37/8

http://functions.wolfram.com/07.23.03.c3nw.01

Input Form

Hypergeometric2F1[11/8, 37/8, -(11/2), z] == -((1/(831488 (1 - z)^(23/2))) (Sqrt[1 - z] (-831488 + 10341632 z - 60510240 z^2 + 224267817 z^3 - 609552885 z^4 + 1419638682 z^5 - 4651315858 z^6 - 3627398195 z^7 + 202976127 z^8 - 21447040 z^9 + 1340440 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + 4 Sqrt[z] (-155904 + 1961792 z - 11614239 z^2 + 43538193 z^3 - 119507695 z^4 + 279664371 z^5 - 1681333383 z^6 - 931572289 z^7 + 53383023 z^8 - 5529315 z^9 + 335110 z^10) Sin[(3 ArcSin[Sqrt[z]])/4]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]